Math 23: Differential Equations

Winter 2013

Turbulence on a Polar Beta-plane (image due to Y. D. Afanasyev & J. Wells)

Look here for more pictures and brief explanations



  Section 01 Section 02
Instructor Craig Sutton Min Hyung Cho
Lectures MWF 11:15-12:20 (108 Kemeny) MWF 12:30-1:35 (007 Kemeny)
X-Hour Tu 12-12:50 (108 Kemeny) Tu 1-1:50 (007 Kemeny)
Office Hours

Tu 2:30-3:30, Fri. 9:30-10:30

(also by appointment)

Mo. 3:00-4:00, Th. 2:00-3:00

(also by appointment)

Office 321 Kemeny Hall 315 Kemeny Hall
E-mail Craig.J.Sutton AT You Know Where Min.H.Cho AT You Know Where
Phone 603-646-1059 603-646-9847
Syllabus, Announcements, HW, etc.

Daily Syllabus Homework

Daily Syllabus Homework

Course Policies & Information Information Information
Tutorials (with Tim Dwyer) Sun., Tues. & Thurs. 7-9PM (105 Kemeny Hall) Sun., Tues. & Thur. 7-9PM (105 Kemeny Hall)


Course Description: Differential equations are equations that relate functions and their higher order (partial) derivatives.
They provide a natural language and set of tools through which we can describe and explore the world around us.
For instance, in mathematics and physics differential equations can be used to describe the path that light will travel in exotic geometries. In engineering differential equations can be used to model how a bridge will twist under stress. And in finance, (stochastic) differential equations are used to help price financial derivatives (e.g, options, futures \& credit derivatives).

This course will focus primarily on methods for obtaining exact solutions to various types of differential equations, but (as time permits) we will also explore means of ferreting out qualitative information about solutions based on the form of the differential equation. Topics will include some of the following.


Prerequisites: Math 13 plus a strong interest in mathematical ideas and their applications. If you are unsure about your preparation please speak with your instructor as soon as possible.

Target Audience: This course should be of interest to students in mathematics, physics, engineering and the social sciences.

Students with Disabilities: If you have a disability and require disability related accomodations please speak to me and Ward Newmeyer, Director of Student Accessibility Services, as soon as possible so we can find a remedy.

Textbook: Elementary Differntial Equations & Boundary Value Problems (Ninth Edition), Boyce & DiPrima, Wiley 2009. (available at Wheelock Books).

Tentative Syllabus: This syllabus is subject to change, but it should give you a rough idea of the topics we will cover this term.



Brief Description

Week 1

1, 2.1- 2.5

First Order ODEs; The Existence & Uniqueness Theorem; Modeling with First Order ODEs; Autonomous Equations and Geometric Methods

Week 2

2.5, 2.7 & 3.1-3.3

Autonomous Eqs. & Geom. Methods; Intro. to Matrix Algebra; Second Order Linear ODEs: the Wronskian & Complex Roots


Week 3

3.4 - 3.8

Second Order Linear ODEs: constant coeff. with repeated roots; Non-homogeneous Equations: method of undetermined coefficients & Variation of Parameters; Mechanical Vibrations


Week 4

5.1- 5.4

Spring-Mass System; Power Series and Series Solutions to ODEs; Euler's Equation


Week 5

5.1-5-5.4 & 7.1-7.4

Series Solutions; Linear Independence; Eigenvalues & Eigenvectors

Week 6

7.4 - 7.8

Systems of First Order Linear ODEs


Week 7

7.1- 7.9, 9.1 & 9.2

Systems of First Order Linear ODEs; Non-Linear Systems

Week 8

9.2-9.4 & 10.1-10.4

Non-Linear Systems; Two-Point Boundary Value Problems; Fourier Series

Week 9
Fourier Series and the heat equation

(tentative) Deliverables & (tentative) Grading Guide & Policies: The following will comprise the written assignments for this term.

GRADING GUIDE: Your final grade will be computed according to the following scheme.

Written HW
Exam 1
Exam 2
Final Exam



Last Updated 4 January, 2013